What is the derivative of ln(sqrt(9-x^2)) ?

The derivative of ln(sqrt(9-x^2)) is -x/(9-x^2)

What is the first derivative of ln(sqrt(9-x^2)) ?

The first derivative of ln(sqrt(9-x^2)) is -x/(9-x^2)

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\frac{d}{d x} (ln (9 - x^{2}))

- \frac{x}{9 - x ^{2}}

Solution steps

\frac{d}{d x} (ln (9 - x^{2}))

Apply the chain rule:

\frac{1}{9 - x ^{2}} \frac{d}{d x} (9 - x^{2})

= \frac{1}{9 - x ^{2}} \frac{d}{d x} (9 - x^{2})

\frac{d}{d x} (9 - x^{2}) = - \frac{x}{9 - x ^{2}}

= \frac{1}{9 - x ^{2}} (- \frac{x}{9 - x ^{2}})

Simplify

\frac{1}{9 - x ^{2}} (- \frac{x}{9 - x ^{2}}) : - \frac{x}{9 - x ^{2}}

= - \frac{x}{9 - x ^{2}}

\frac{\partial}{\partial x} (x^{2} + y^{2} + z^{2} - 1)

arccos (\frac{cos ( x )}{1 + cos ( x )})

f (x) = sin (8 x)

y = x^{9 c o s (x)}

\int 2 - ∣ x ∣ d x

What is the derivative of ln(sqrt(9-x^2)) ?
The derivative of ln(sqrt(9-x^2)) is -x/(9-x^2)
What is the first derivative of ln(sqrt(9-x^2)) ?
The first derivative of ln(sqrt(9-x^2)) is -x/(9-x^2)